The Solution of Equations
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In our eReader you can find the full English version of the book. Read The Solution of Equations Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Solution of Equations
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9). Now sin 3(9 being computed, 36^ is found from a table of sines, and then d is known. Thus, ;/, =: 2r sin 6, /, = 2r sin (120° + ff), y^ ~ 2r sin (240° + ^, are the real roots of the cubic in y.\ * For an outline of these transcendental methods, see Hagen's Synopsis der hoheren Mathematik, Vol. I, pp. 339-344.
f When B^ is negative and numerically less than C, as also when B* is positive, this solution fails, as then one root is real and two are imaginary. In this case, however, a similar me...thod of solution by means of hyperbolic sines is possible. See Grunert's Archiv fur Mathematik und Physik, Vol. xxxviii, pp. 48-76.
TRIGONOMETRIC SOLUTIONS. 25 For example, the depth of flotation of a sphere whose diam- eter is 2 feet and specific gravity 0.65, is given by the cubic equation x^ — 3^" + 2.6 = o (Art. 6). Placing x=y-\-\ this reduces to y — ly ■\- 0.6 — o, for which B = — \ and C =+0.3.
Thus r = I and sin 3^ = -(-0.3. Next from a table of sines, 36/ = 17° 27', and accordingly = s° 49'.
What to read after The Solution of Equations?
You can find similar books in the "Read Also" column, or choose other free books by Mansfield Merriman to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
9). Now sin 3(9 being computed, 36^ is found from a table of sines, and then d is known. Thus, ;/, =: 2r sin 6, /, = 2r sin (120° + ff), y^ ~ 2r sin (240° + ^, are the real roots of the cubic in y.\ * For an outline of these transcendental methods, see Hagen's Synopsis der hoheren Mathematik, Vol. I, pp. 339-344.
f When B^ is negative and numerically less than C, as also when B* is positive, this solution fails, as then one root is real and two are imaginary. In this case, however, a similar me...thod of solution by means of hyperbolic sines is possible. See Grunert's Archiv fur Mathematik und Physik, Vol. xxxviii, pp. 48-76.
TRIGONOMETRIC SOLUTIONS. 25 For example, the depth of flotation of a sphere whose diam- eter is 2 feet and specific gravity 0.65, is given by the cubic equation x^ — 3^" + 2.6 = o (Art. 6). Placing x=y-\-\ this reduces to y — ly ■\- 0.6 — o, for which B = — \ and C =+0.3.
Thus r = I and sin 3^ = -(-0.3. Next from a table of sines, 36/ = 17° 27', and accordingly = s° 49'.
What to read after The Solution of Equations?
You can find similar books in the "Read Also" column, or choose other free books by Mansfield Merriman to read onlineMoreLess
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